Let \(\displaystyle f:[-3,-2) \cup(-2, \infty) \rightarrow R, f(x)=1+\frac{1}{x+2}\). --- 0 WORK AREA LINES (style=lined) --- --- 3 WORK AREA LINES (style=lined) --- a. b. \(x\in [-3, -2)\cap (-1, \infty)\) a. b. \(\text{From graph }f(x)\leq -2\ \text{ for}\ -3\leq x <2\ \text{ and when }\ x\geq -1\) \(\rightarrow x\in [-3, -2)\cap (-1, \infty)\)
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Graphs, MET2 2022 VCAA 2 MC
The graph of `y=\frac{1}{(x+3)^2}+4` has a horizontal asymptote with the equation
- `y=4`
- `y=3`
- `y=0`
- `x=-2`
- `x=-3`
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From graph
`=>A`
Graphs, MET2 2020 VCAA 5 MC
The graph of the function `f:D rarr R,f(x)=(3x+2)/(5-x)`, where `D` is the maximal domain, has asymptotes
- `x=-5,y=(3)/(2)`
- `x=-3,y=5`
- `x=(2)/(3),y=-3`
- `x=5,y=3`
- `x=5,y=-3`
Graphs, MET1 2021 VCAA 4
- Sketch the graph of `y = 1 - 2/(x - 2)` on the axes below. Label asymptotes with their equations and axis intercepts with their coordinates. (3 marks)
- Find the values of `x` for which `1 - 2/(x - 2) >= 3`. (1 mark)
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a.
b. `x in [1, 2)`
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a. `text(Asymptotes:)`
`x=2`
`text(As)\ \ x→ +-oo, \ y→1\ \ =>\ text(Asymptote at)\ \ y=1`
`ytext(-intercept at)\ (0,2)`
`xtext(-intercept at)\ (4,0)`
♦ Mean mark part (b) 32%.
b. `text(By inspection of the graph:)`
`1-2/(x-2) >=3\ \ text(for)\ \ x in [1, 2)`
Graphs, MET2-NHT 2019 VCAA 4 MC
The graph of the function `ƒ : D → R, \ f(x) = (2x -3)/(4 + x)`, where `D` is the maximal domain, has asymptotes
- `x = –4, \ y = 2`
- `x = (3)/(2), \ y = –4`
- `x = –4, \ y = (3)/(2)`
- `x = (3)/(2), \ y = 2`
- `x = 2, \ y = 1`